Bullseye illusion

The blue ring is formed by the difference in area between a larger circle with radius c and a smaller circle with radius b.

Let the green circle have radius a. Then the condition for the equality of the two areas is:

${\displaystyle \pi a^{2}=\pi c^{2}-\pi b^{2}}$, i.e.,

${\displaystyle a={\sqrt {c^{2}-b^{2}}}}$.

For the special case ${\displaystyle a=b}$ (Figure 4), the condition for the equality of the two areas is:

${\displaystyle \pi b^{2}=\pi c^{2}-\pi b^{2}}$, i.e.,

${\displaystyle a=b={\frac {c}{\sqrt {2}}}}$.

In this case, the larger circle is completely decomposed into the smaller green circle and the blue ring of equal area.^[1][2]

• Bullseye illusion Wolfram MathWorld
• Bullseye illusion (interactive demonstration) Wolfram Demonstrations Project
• Bullseye optical illusion from math-fail.com